PACE: Parameter-Efficient Calibration for Robust Posterior Inference under Simulator Misspecification

Simulator based inference provides a framework for inferring parameters of complex stochastic simulators in the absence of explicit likelihood. However, misspecification in the simulator often creates systemic discrepancies, which leads to poor posterior estimates for real data samples. Recent works have attempted to address this by explicitly handling the discrepancy using methods such as transport-based correction, or robust summary learning. However, this involves additional objectives or multi-stage procedures. We show that, surprisingly, such elaborate adaptation is often not required in many cases of practical interest. We introduce PACE, a simple and deliberately minimal calibration strategy for simulator-pretrained neural posterior inference.Rather than defining explicit correction mechanisms, PACE leverages the representation and posterior structure learnt using abundant simulated data and calibrates the posterior using light weight feature wise transformations learnt using a small set of labeled real observations. These light-weight transformations are parameterized using a small set of calibration parameters and optimized directly for posterior inference. Despite its compact calibration space and simple strategy, PACE demonstrates effective outcome across diverse data modalities ranging from time-series to images. On multiple evaluation metrics, PACE yields comparable or better results than SOTA approaches while requiring adaptation of a very small number of parameters. Our results suggest that when simulation-trained representations retain the information required for posterior inference, expensive re-learning or explicit alignment to the target distribution is unnecessary and a lightweight calibration of existing inference pathway suffices.